You are missing the point.
The time has never been in a consistent flow:
Loop A affects Loop B which affected Loop C, until the Loop "stabilizes" at C as an infinite Loop.
The original time line Reese was never the father, and Connor had a different father. Skynet had an original launch date that had nothing to do with CyberDyne. This is how Terminator 3 can exist - the original launch date. This is Loop A.
In Loop B, a Terminator is sent back, and failed for whatever reasons; he might have killed Sarah for that matter but John Connor was already born. Hence why he was even alive to possibly send Reese, although it is not necessary.
In Loop C, upon knowing what happens in Loop B Connor probably wants to save his mother. So he sends back Reese.
Thus, within Loop C is the official infinite branch off. But it is nothing like the original history. Terminator 2 of course introduces more loops and complex relationships but it works.